Statistics and Probability Answers

) An experiment is run in the following manner.The colors red, yellow, and blue are each flashed on a screen for a short period of time. A subject views the colors and is asked to choose the one he feels was flashed for the longest amount of time. The experiment is repeated three times with the same subject. If all the colors were flashed for the same length of time, give the probability distribution for y, the number of times the subject choose the color red. Assume that his three choice are independent

A box contains ten light bulbs of which four are defective. A bulb is selected from the box and tested. If it is defective, another bulb is selected and tested, until a non-defective bulb is chosen. Let the random variable X be the number of bulbs chosen. 

a) Write sample space for this random experiment?

b) Find probability mass Function of X? 

c) Find CDF of X?

To verify whether a course in statistics improved performance, a similar test was given to 12 participants both before and after the course. The original grades recorded in alphabetical order of the participants were 44. 40, 61, 52, 32, 44, 70, 41, 67, 72, 58 and 72. After the course, the grader were in the same order 58. 38, 68, 87, 46, 39. 78, 48, 78, 74, 60 and 78.

(a) Was the course useful, as measured by performance on the test? Consider these 12 participants as a sample from a population.

(b) Would the same conclusion be reached if tests were not considered paired?Use 5% level of significance in both cases

If Z is a standard normal random variable, what is the value z for which P(0 ≤ Z ≤ z) = 0.35

From the area pianted in one variety of guayule, 54 plants were selected at random. Of these plants. 15 were "Offrypes" and 12 were "Aberrants. The rubber per centages of these plants were:

Offtypes4.47, 5.88, 6.21, 5.55, 6.09, 5.70, 5.82, 4.84, 5.59, 5.59,5.22. 4.45, 6.74. 6.06, 6.04· Aberrants 6.48, 6.36, 4.2S, 7.71, 6.40, 7.06, 5.02, &.93. 7.72, 7.20,7.37, 5.91

Compute a 90% confidence interval for the difierence of two population means.

Question

In a certain experiment to compare two types of sheep food A and B, the following results of increase in weights were observed:

Sheep No. 1 2 3 4 5 6 7 8

Food A 49 53 51 52 47 50 52 53

Food B 52 55 52 53 50 54 54 53

Weight (in kg)

450 380 250 220 260 302 280 302

Answer the following questions

a) Assuming that two sample of sheep are independent, can we conclude that food B is better than food A?

b) Examine the case when the same sets of eight sheep were used in both the foods?

c) Determine 98% confidence interval for Food A and B when assuming that two sample of sheep are independent?

d) Determine 95% confidence interval for Food A and B when assuming that two

The mean lifetime of a sample of 100 light tubes produced by a company is found to be 1570 hours with standard deviation of 80 hours. Test the hypothesis that the mean lifetime of the tubes produced by the company is 1600 hrs.

The mean annual wage of male workers in a particular company was Ksh. 67952 and that of female workers was Ksh. 61295 each year. The standard deviation for the two samples is Ksh. 3202 and Kshs.3758, respectively. Assuming the measurements are from random samples of 24 males and 27 we want to investigate whether the mean salary of males is higher than that of females at α=0.05. Find:

a. The test statistic 𝑍𝑐

b. Remember that the Null hypothesis will be rejected if 𝑍𝑐 > 𝑍𝑡 . Give the value of 𝑍�

Scores made by students in a statistics class in the mid-term and final examination are given here. Develop a regression equation which may be used to predict final examination scores from the midterm score. (Hint: The regression equation is given as 𝑌̂ = 𝑎 + 𝑏𝑥.)

Student 1 2 3 4 5 6 7 8 9 10

Mid Term (x) 94 60 96 94 81 40 70 50 72 70

Final (y)(y) 87 73 94 87 76 61 77 71 84 77

A study was conducted to find whether there is any relationship between the weight and blood pressure of an individual. The following set of data was arrived at from a clinical study. The first column represents the serial number and the second and third columns represent the weight and blood pressure of each patient.

Weight (x) 65 82 71 73 63 72 71 77 71 77

Blood Pressure (y)(y) 136 145 123 132 175 165 152 158 117 129

Find the coefficient of correlation for this set of data.